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Question
If a + b + c = 9 and ab + bc + ca = 40, find a2 + b2 +c2.
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Solution
Recall the formula
`(a+b+c)^2 = a^2 +b^2 +c^2 +2(ab +bc+ca)`
Given that
`(a+b+c) = 9,ab + bc + ca = 40`,
Then we have
`(a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)`
` ( 9)^2 = a^2 + b^2 + c^2 + 2.( 40) `
`a^2 ++ b^2 + c^2 + 80 = 81`
`a^2 + b^2 + c^2 = 81 - 80
`a^2 + b^2 +c^2 =` 1
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